Make the sign a 3D layer, move the pivot for the layer to the left side of the door where the hinges are, then position the sign back in the middle of the door, leaving the pivot off to the side. Now as the door opens and closes you should be able to use your X rotation channel to move the sign with the door, replete with perspective changes, without doing any painful manual tracking. That said, I don’t know if there is a way to compensate for various camera lenses in AFX, out of the box.
Hope that helps.
-Dustin